How do I attach floating vertices to the mesh?
To join the floating vertices to the rest of the mesh, you would need to delete the faces sitting in the area, select adjacent vertices then press F. This will fill in edges between the vertices, and once you've gotten all the lines, you can fill in the faces by selecting edges and pressing F.



There are a couple of ways you could have gone about doing this differently though. The first way would be using the Cut Through option for the knife tool. You'd use it by first pressing 3 on the Numpad to enter the side orthographic view, pressing K to enable the knife tool, than Z to toggle cutting through. What this will do is create the cuts on all parts of the meshes that your cutting lines project onto, including the far side of the turbine.



A better way to have gone about modelling it would be deleting half of the turbine and applying a Mirror modifier to reflect the object across its origin, thereby cutting the modelling time in half.